Question

Given the following data, estimate the coefficient of QD:
15, 20, 23, 23, 25, 25, 27, 40

Answer 1

Given data series:
15, 20, 23, 23, 25, 25, 27, 40
Here, N = 8
$$\begin{gathered} Q_1=\mathrm{size}\mathrm{of}{\left(\frac{8+1}{4}\right)}^{th}=\mathrm{size}\mathrm{of}2.{25}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{size}\mathrm{of}{2}^{nd}\mathrm{item}+0.25\left(\mathrm{size}\mathrm{of}{3}^{rd}\mathrm{item}-\mathrm{size}\mathrm{of}{2}^{nd}\mathrm{item}\right) \\ =20+0.25\left(23-20\right)=20.75 \\ {Q}_3=\mathrm{size}\mathrm{of}3{\left(\frac{8+1}{4}\right)}^{th}\mathrm{item}=\mathrm{size}\mathrm{of}6.{75}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{size}\mathrm{of}{6}^{th}\mathrm{item}+0.75\left(\mathrm{size}\mathrm{of}{7}^{th}\mathrm{item}-\mathrm{size}\mathrm{of}{6}^{\mathrm{th}}\mathrm{item}\right) \\ =25+0.75\left(27-25\right)=26.5 \end{gathered}$$
$\mathrm{Coefficient}\mathrm{of}\mathrm{Q}.\mathrm{D}.=\frac{Q_3-Q_1}{Q_3+Q_1}=\frac{26.5-20.75}{26.5+20.75}=0.121$